RICHMOND — The City Council is taking applications for its next member, but the dais is so divided that it appears unlikely that council members will be able to agree on the right person for the job.

The council on Thursday night set a Jan. 31 deadline for candidates to declare interest in being appointed to a seat rendered vacant by the illness of Gary Bell, who was elected Nov. 6 but remains hospitalized in a coma after a severe sinus infection and two neurosurgeries.

Two council members, Corky Boozé and Nat Bates, did not attend the meeting, saying they were “disrespected” by Mayor Gayle McLaughlin, who scheduled the meeting despite both men having prior engagements. But McLaughlin noted that the process must be set now to ensure that the city could hold a special election if no appointment is made.

Candidates must file a statement of interest to be considered, and the council will convene Feb. 4 to hear comments from candidates and the public before voting on an appointment.

Five people have said they will file for the spot, and more may emerge before the deadline.

But whether any of the candidates can get a majority of the six-member council’s votes remains in doubt.

“This council has never agreed in that way, ever,” resident Garland Ellis said.

If no one gets four votes for appointment Feb. 4, the city will hold a special election June 4. McLaughlin said an election would cost the city about $100,000, even with savings realized by consolidating the issue with a West Contra Costa School District ballot measure.

“It’s still a hefty amount in my view,” McLaughlin said.

McLaughlin and council members Jovanka Beckles and Tom Butt are likely to back appointing Eduardo Martinez, who finished less than 1 percentage point behind Bell in November. Martinez is a member of the Richmond Progressive Alliance, which also supports McLaughlin and Beckles. The seat was in play because RPA member Jeff Ritterman declined to run for re-election.

Councilmen Bates and Boozé have said they will not support Martinez, an environmental advocate who ran on a starkly different platform from the Chevron-supported Bell. The battle over the seat and the polarization of the council figure to intensify in the coming weeks.

In a prepared statement read to the council by City Clerk Diane Holmes, Bates alleged that McLaughlin and her council allies were cynically seizing on Bell’s illness to subvert the will of the voters and enlarge their political power.

“I not only represent members of the African-American community but a large portion of the community at large, and to silence their voices through denying my participation is disrespectful and I consider it a personal insult,” Bates wrote.

Councilman Jim Rogers, the potential fourth vote for Martinez, said Thursday he has not decided whether to vote for Martinez or any other candidate. Rogers noted that $100,000 was a tiny fraction of the city’s overall expenditures.

More than a dozen speakers Thursday demonstrated the divide over whether to appoint a candidate or put the issue back to voters.

“We’ve seen how difficult it is to get public business done with six (council) members,” said resident Marilyn Langlois, who urged the council to appoint Martinez.

“Let’s let the voters vote,” said resident Rosa Lara, who added that Martinez represented a stark difference from the voters’ choice of Bell.

The vacant spot could alter the balance of power in the city, which has been dominated by the progressives since 2010. An appointee would have to run for re-election in 2014, but the winner of a special election in June would hold the seat for four years.

In addition to Martinez, Kathleen Sullivan, Don Gosney, Mike Ali-Kinney and Jael Myrick have announced their candidacies. Former Councilman John Marquez said Thursday he was also considering a run. Sullivan has the support of the local African-American political action groups that supported Bell.

If the council does not appoint a candidate at the special meeting Feb. 4, it must call for the special election on Feb. 5 in compliance with state law, which says special elections must be called at least 114 days before voters go to the poll, McLaughlin said.

At the Feb. 4 meeting, each candidate will be given eight minutes to make their case to the council for why they would be the best fit for the appointment.